Question

Un biciclist a plecat intr-o excursie din orasul A in orasul B.Prima jumatate de drum a mers cu viteza V1 = 12 km/h. Jumatate din timpul ramas a mers cu viteza V2 = 8,0 km/h iar restul drumului a mers pe jos cu viteza V3 = 4,0 km/h. Care a fost viteza medie a biciclistului?

Answer 1

$\it v = \dfrac{d}{t} \Rightarrow t = \dfrac{d}{v}\\ \\ \\ t_1=\dfrac{\dfrac{d}{2}}{12}=\dfrac{d}{24}\\ \\ \\ t_2=\dfrac{\dfrac{d}{4}}{8}=\dfrac{d}{32}\\ \\ \\ t_3=\dfrac{\dfrac{d}{4}}{4}=\dfrac{d}{16}$

$\it t_1+t_2+t_3=d\left(\dfrac{1}{24}+\dfrac{1}{32}+\dfrac{1}{16}\right)=d\cdot\dfrac{1}{8}\cdot\left(\dfrac{^{4)}1}{\ 3}+\dfrac{^{3)}1}{\ 4}+\dfrac{^{6)}1}{\ 2}\right)=\\ \\ \\ =d\cdot\dfrac{1}{8}\cdot\dfrac{13}{12} =d\cdot\dfrac{13}{96}\\ \\ \\ v_m=\dfrac{d}{t_1+t_2+t_3} =\dfrac{d}{d\cdot\dfrac{13}{96}} =\dfrac{1}{\dfrac{13}{96}}=\dfrac{96}{13}\approx 7,4\ km/h$